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authorThibaut Horel <thibaut.horel@gmail.com>2015-02-06 15:48:24 -0500
committerThibaut Horel <thibaut.horel@gmail.com>2015-02-06 15:48:24 -0500
commit0ff14f56819acfc7be77f9237e18417d465b2266 (patch)
tree32576d399ce36de031188e1ffff5b8e3f56b4336 /paper/sections/model.tex
parent724dae4487559d7e52c5ac56b9059d124b664a13 (diff)
downloadcascades-0ff14f56819acfc7be77f9237e18417d465b2266.tar.gz
Compression
Diffstat (limited to 'paper/sections/model.tex')
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1 files changed, 2 insertions, 3 deletions
diff --git a/paper/sections/model.tex b/paper/sections/model.tex
index 36829f2..d8706bc 100644
--- a/paper/sections/model.tex
+++ b/paper/sections/model.tex
@@ -12,8 +12,7 @@ state space $\{0, 1, \dots, K-1\}^V$ with the following properties:
that all transition probabilities of the Markov process are either constant
or can be expressed as a function of the graph parameters $\Theta$ and the
set of ``contagious nodes'' at the previous time step.
-\item The initial probability over $\{0, 1, \dots, K-1\}^V$ of the Cascade
- Model is such that all nodes can eventually reach a \emph{contagious state}
+\item The initial probability over $\{0, 1, \dots, K-1\}^V$ is such that all nodes can eventually reach a \emph{contagious state}
with non-zero probability. The ``contagious'' nodes at $t=0$ are called
\emph{source nodes}.
\end{enumerate}
@@ -26,7 +25,7 @@ the ``single source'' assumption made in \cite{Daneshmand:2014} and
\cite{Abrahao:13} as well as the ``uniformly chosen source set'' assumption
made in \cite{Netrapalli:2012} verify condition 3.
-In the context of Graph Inference, \cite{Netrapalli:2012} focuses specifically
+In the context of Graph Inference, \cite{Netrapalli:2012} focus
on the well-known discrete-time independent cascade model recalled below, which
\cite{Abrahao:13} and \cite{Daneshmand:2014} generalize to continuous time. We
extend the independent cascade model in a different direction by considering